The present invention relates to a method for generating a curved surface by a curved surface generator such as CAD, CAM, etc., and particularly relates to a curved surface generating method and an apparatus therefor, which are suitable for generating a curved surface designed by an operator, through a simple procedure.
CAD/CAM systems have been popularized so that designed furnishings, cars, industrial arts and the like have been drawn by a computer. In the case where a designer uses such a conventional system to express an image of a certain shape, first a shape approximating to the target shape is drawn by shape feature line groups and then these line groups are decomposed or auxiliary lines are added thereto so that the image is expressed as tetragonal nets generated in three-dimensional space. For example, such nets are expressed by line groups constituting sides of tetragons and are called "wire frame". Then, a curved surface called "tetragonal patch" is generated correspondingly to each of the tetragons constituting the wire frame. Further, adjacent tetragonal patches are connected to one another so smoothly as to form a curved surface on the whole of the wire frame. In the case where each tetragonal patch is generated, a point on the patch is expressed by a vector function on the basis of the rule of smoothly changing opposite sides of a tetragon from one to the other. As the vector function, used is a Bezier or B-spline three-order equation having two parameters because the calculation thereof is easy.
In the case where adjacent tetragonal patches are connected to one another so smoothly as to form a curved surface, a considerably complex process is required. Further, it is difficult that a formative structure having an end portion greatly distorted in shape is sufficiently expressed by the tetragonal wire frame (three-dimensional graph). Therefore, as described in Japanese Patent Unexamined Publication JP-A-63-159982, a wire frame is generated so as to contain trigonal patches as well as tetragonal patches to thereby smoothly generate a curved surface in the trigonal and tetragonal patches contained in the wire frame. Further, as described in Japanese Patent Unexamined Publication JP-A-61-265675, curved surface patches being constantly lifted or dented to locally modify the wire frame are generated again in the case where a curved surface once generated is out of the target shape.